7 papers
Lacunary hyperbolic groups with fast injectivity radius growth and enough loxodromic elements are selfless
Goulnara Arzhantseva, Martin Finn-Sell
We prove that a lacunary hyperbolic group with sufficient generics is selfless in the sense of Amrutam--Gao--Kunnawalkam Elayavalli--Patchell, provided the hyp…
Representation theory of topological full groups of étale groupoids and paradoxicality
Vadim Alekseev, Martin Finn-Sell
We provide a unified treatment of several results concerning full groups of ample groupoids and paradoxical decompositions attached to them. This includes a criterion for the full…
Controlled Analytic Properties and the Quantitative Baum-Connes Conjecture
Martin Finn-Sell
We show that the classical Baum-Connes assembly map is quantitatively an isomorphism for a class of lacunary hyperbolic groups, and we explain how to see that this class contains m…
Unrestricted wreath products and sofic groups
Goulnara Arzhantseva, Federico Berlai, Martin Finn-Sell +1
We show that the unrestricted wreath product of a sofic group by an amenable group is sofic. We use this result to present an alternative proof of the known fact that any group ext…
Sofic boundaries of groups and coarse geometry of sofic approximations
Vadim Alekseev, Martin Finn-Sell
Sofic groups generalise both residually finite and amenable groups, and the concept is central to many important results and conjectures in measured group theory. We introduce a to…
Non-amenable principal groupoids with weak containment
Vadim Alekseev, Martin Finn-Sell
We construct examples of principal groupoids that have weak containment but are not amenable, thus answering questions by Claire Anantharaman-Delaroche and Rufus Willett.